D) Following is forecast for economic situation and Rachel’s portfolio returns next year, calculate the
expected return, variance and standard deviation of the portfolio. (4 marks)
State of economy Probability Rate of returns
Mild Recession 0.35 - 5%
Growth 0.45 15%
Strong Growth 0.20 30%

Expected return = 15.25%

Variance = 80.31

Standard deviation =  8.961

Explanation:

Expected value of return (Er) =

(0.35 × 5%) + (0.45× 15%) + (0.20 × 30%)= 15.25 %

Variance and standard deviation

  Outcome      Rate   Deviation  Variance

                                    r- Er         (r-Er)^2.P

Mild               5          -10.25        36.771875

Growth         15          -0.25         0.028125

Strong          30            14.75        43.5125

Total                                                80.3125

Variance = 80.3125

Standard deviation = √variance = √80.3125

                             =  8.96

Expected return = 15.25%

Variance = 80.31

Standard deviation =  8.961

answer: marginal utility of the fourth brownie is 0.

explanation: marginal utility is the addtional utility gained from the consumption of one more unit of a good. it is given by,

so, marginal utility at the 4th unit will be given by

since, the values are not given here, you can simply find marginal utility at fourth unit by subtracting total utility at 3rd unit from total utility at 4th unit.